Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×C4⋊AGL(1,𝔽5) | C2 | semidirect |
| 3. C5×D5⋊M16 | C2 | semidirect |
| 4. C5×#4009 | C2 | semidirect |
| 5. C5×#4007 | C2 | semidirect |
| 7. C52×#41 | C4 | semidirect |
| 8. C5×#713 | C4 | semidirect |
| 11. C5×#711 | C4 | semidirect |
| 15. C5×#709 | C4 | semidirect |
| 23. #65793 | C5 | direct (N × H) |
| 29. C52×Q8 | C2×C4 | semidirect |
| 31. C52×D4 | C2×C4 | semidirect |
| 40. C5×D20 | C2×C4 | semidirect |
| 49. C5×Dic10 | C2×C4 | semidirect |
| 53. C2×C4⋊AGL(1,𝔽5) | C2×C5 | semidirect |
| 54. D5⋊M16 | C2×C5 | semidirect |
| 57. #4009 | C2×C5 | semidirect |
| 58. #4007 | C2×C5 | semidirect |
| 84. C5×#41 | C4×C5 | semidirect |
| 85. C5×#41 | AGL(1,𝔽5) | semidirect |
| 92. #713 | C4×C5 | semidirect |
| 95. #711 | C4×C5 | semidirect |
| 99. #709 | C4×C5 | semidirect |
| 129. C5×Q8 | C2×C4×C5 | semidirect |
| 130. C5×Q8 | C2×AGL(1,𝔽5) | semidirect |
| 140. C5×D4 | C2×C4×C5 | semidirect |
| 141. C5×D4 | C2×AGL(1,𝔽5) | semidirect |
| 165. D20 | C2×C4×C5 | semidirect |
| 174. Dic10 | C2×C4×C5 | semidirect |
| 182. C52 | #417 | semidirect |
| 225. #41 | C5×AGL(1,𝔽5) | semidirect |
| 258. Q8 | C2×C5×AGL(1,𝔽5) | semidirect |
| 265. D4 | C2×C5×AGL(1,𝔽5) | semidirect |
| 281. C5 | C5×#417 | semidirect |
| 282. C5 | #65793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×#41 | 2 |
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C5×D5⋊M16 | 2 |
| C5×#4009 | 2 |
| C5×#4007 | 2 |
| #65793 | 5 |
| C5×#417 | 5 |